In this work, we uncover non-Hermiticity induced spectral, localization
and topological phase transitions in the nonreciprocal Maryland model.
A transformation of the system from a localized phase with real spectrum
to a mobility edge phase with complex spectrum can be obtained only
if there are finite amounts of hopping asymmetry. The equations satisfied
by the complex spectrum, phase boundaries and energy-dependent mobility edges are found
exactly. A topological order parameter is further employed to build
the phase diagram and characterize transitions between different NHQC
phases. Notably, due to the unbounded nature of
onsite potential in the NRMM, we find no extended phases
at any finite hopping nonreciprocity, which is distinct
from the situation found in a Maryland model with complex onsite
potential [1]}. Our study thus enriches the family of NHQCs
by unveiling a particular type of system with only localized
and mobility edge phases, whose properties can be characterized
exactly.
